Related papers: The translation operator for self-projective coalg…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
A $K^\alpha$-translator is a surface in Euclidean space $\r^3$ that moves by translations in a spatial direction and under the $K^\alpha$-flow, where $K$ is the Gauss curvature and $\alpha$ is a constant. We classify all…
This paper is devoted to self-adjoint cyclically compact operators on Hilbert--Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators are given. We apply this result to partial…
We introduce the notion of Rota-Baxter coalgebra which can be viewed as the dual notion of Rota-Baxter algebra. We provide some concrete examples and establish various properties of this new object. We also consider comodules over…
The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and…
This is the second paper of a series of papers on a version of categories $\mathcal{O}$ for root-reductive Lie algebras. Let $\mathfrak{g}$ be a root-reductive Lie algebra over an algebraically closed field $\mathbb{K}$ of characteristic…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We generalize the work by Soboci\'nski on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our…
We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the…
By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.
A collectively $\sigma$-Levi set of operators is a generalization of the $\sigma$-Levi operator. By use of collective order convergence, we investigate relations between collectively $\sigma$-Levi and collectively compact sets of operators.
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…
In this paper an asymmetrical operator of generalised translation is introduced, the generalised modulus of smoothness is defined by its means and the direct and inverse theorems in approximation theory are proved for that modulus. ----- V…
The decomposition of polynomials of one vector variable into irreducible modules for the orthogonal group is a crucial result in harmonic analysis which makes use of the Howe duality theorem and leads to the study of spherical harmonics.…
In this paper we study self-adjoint commuting ordinary differential operators. We find sufficient conditions when an operator of fourth order commuting with an operator of order $4g+2$ is self-adjoint. We introduce an equation on…
We adapt techniques used in the study of the cubic Dirac operator on homogeneous reductive spaces to the Dolbeault operator on elliptic coadjoint orbits to prove that cohomologically induced representations have an infinitesimal character,…
Subaddivity type matrix inequalities for concave funcions and symetric norms are given.
The paper derives a new "position translation vector" (PTV) with remarkably simpler rate equation, and proves its connections with Savage's PTV.
Several algebraic and topological properties of subgradient projection operators are investigated and various examples are provided. Connections with Moreau's proximity operator are also made and acceleration schemes for subgradient…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.